An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to...

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Main Authors: Diego I. Gallardo, Mário de Castro, Héctor W. Gómez
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
bell distribution
EM algorithm
long-term survival model
maximum likelihood
model comparison
Online Access:https://www.mdpi.com/2227-7390/9/15/1815
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spelling doaj-a703da0767e441e0959b0e5a5400c0b22021-08-06T15:28:30ZengMDPI AGMathematics2227-73902021-07-0191815181510.3390/math9151815An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma DataDiego I. Gallardo0Mário de Castro1Héctor W. Gómez2Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, BrazilDepartamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileA cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.https://www.mdpi.com/2227-7390/9/15/1815bell distributionEM algorithmlong-term survival modelmaximum likelihoodmodel comparison
collection DOAJ
language English
format Article
sources DOAJ
author Diego I. Gallardo
Mário de Castro
Héctor W. Gómez
spellingShingle Diego I. Gallardo
Mário de Castro
Héctor W. Gómez
An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
Mathematics
bell distribution
EM algorithm
long-term survival model
maximum likelihood
model comparison
author_facet Diego I. Gallardo
Mário de Castro
Héctor W. Gómez
author_sort Diego I. Gallardo
title An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
title_short An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
title_full An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
title_fullStr An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
title_full_unstemmed An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data
title_sort alternative promotion time cure model with overdispersed number of competing causes: an application to melanoma data
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-07-01
description A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.
topic bell distribution
EM algorithm
long-term survival model
maximum likelihood
model comparison
url https://www.mdpi.com/2227-7390/9/15/1815
work_keys_str_mv AT diegoigallardo analternativepromotiontimecuremodelwithoverdispersednumberofcompetingcausesanapplicationtomelanomadata
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